In this paper, we will develop a tool to analyze polling systems with the autonomous-server, the time-limited, and the k-limited service discipline. It is known that these disciplines do not satisfy the well-known branching property in polling system, therefore, hardly any exact result exists in the literature for them. Our strategy is to apply an iterative scheme that is based on relating in closed-form the joint queue-length at the beginning and the end of a server visit to a queue. These kernel relations are derived using the theory of absorbing Markov chains. Finally, we will show that our tool works also in the case of a tandem queueing network with a single server that can serve one queue at a time.
|Title of host publication||The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools)|
|Place of Publication||Gent, Belgium|
|Number of pages||10|
|Publication status||Published - 2008|
|Publisher||Institute for Computer Sciences, Social-Informatics and Telecommunications Engineering (ICST)|
Al Hanbali, A., de Haan, R., Boucherie, R. J., & van Ommeren, J. C. W. (2008). Time-limited and k-limited polling systems: a matrix analytic solution. In The 3rd International Workshop on Tools for Solving Structured Markov Chains (SMCTools) (pp. -). Gent, Belgium: ICST. https://doi.org/10.4108/ICST.VALUETOOLS2008.4378